When the general principle is not enough

In 1922 Richard Reti published the study given below. A deceptively simple rook and pawn ending at first glance, but infact a brilliant creation, so typical of the genius of Reti.

Reti's study revolves around a rook retreat that is not at all intuitive. Where does white retreat his rook?

If White makes the natural retreat (d1), he will only draw!

1. Rd1(?) A curious exception to the principle that the rook should move as far away as possible (so as to avoid being harrassed by the king). Now, amazingly, White can no longer force a win!


1...d4 2. Kd7 Kd5 3. Kc7 Kc5! Black elbows out the White King. He can not advance.





If he returns to d7, then Black simply repeats the position. So it appears that the normal course of play is 4. Kb7 Kc4 5. Kc6 d3!

The game is now drawn since the Black King will win the White Rook for his pawn. The White King was unable to assist in any meaningful manner since Black succeeded in blocking his advance.

The correct solution to this study is to not retreat the Rook to the back rank immediately, but instead to wait a move:

1. Rd2!! (retreating to d3 is equivalent)




This is the key to the position! By White deliberately losing a tempo, Black will be unable to block out White's King. Paradoxical!

1... d4 2. Rd1!! Only now does White retreat his rook to the back rank!




2...Kd5 (If 2...Ke4 then the reader can verify for himself that after 3.Kd6! Black will lose his pawn) 3. Kd7

Now we see the difference: compared to the variation where White had retreated his rook to d1 immediately, we have reached the same position, but instead of White having the move, it is Black to move!! And this makes all the difference since now the White King can zig-zag in and catch the Black pawn.

Play continues 3...Kc4 ( or if 3... Ke4 4. Kc6! d3 5. Kc5 Ke3 6. Kc4 d2 7. Kc3 winning the pawn)

4. Ke6 d3 5. Ke5 Kc3 6. Ke4 d2 7. Ke3 [1:0] White wins the Black pawn.

Summing up: Reti brought to our attention an entirely new class of rook and pawn ending, where the natural rook retreat is wrong. This kind of goes against our own intuition, and seems to be an exception to the general principle that the rook should be placed as far away as possible.

In praxis it is extremely rare to see this class of ending. However, in the 14th game of the 2000 World Championship match between Kramnik and Kasparov, this class of ending could have been reached over the board! Unfortunately, it did not happen because the players avoided it (for the wrong reasons!) and the game ended prematurely in a draw, depriving the spectators of a really nice example.

The endgame was later analyzed and published by the players' teams...BUT IT WAS ALL INCORRECT, and their conclusions therefore faulty. However, the French endgame specialist and author , Alain Villeneuve, took a very close look at this endgame, and published the correct analysis on the internet. What follows is, essentially, thanks to him! http://www.france-echecs.com/index.php?mode=showComment&art=20061225181612247

(See end of article for more information regarding links)

Kramnik - Kasparov

14th match game for the World Championship in 2000

In this White is fighting for his life: the Black pawn is far advanced and White's pawn is still on the 3rd rank. However, despite this, the game should be a draw with correct play. Clearly White must not exchange rooks. But where should White retreat his rook?

Just as in the Reti study, the natural retreat (f8) is incorrect, and in this particular position , even loses.

1. Rf8? The logical move, but the wrong move! As we shall soon see, moving the rook to f7 would have held the game.

Play would continue 1...Kd2! (Black threatens to advance his pawn) 2. Rd8! Ke1 3. Re8 Rd2 4. Kf3 Rf2!! A very strong move. White's next move is forced

5. Kxe3 ( White loses without a fight after 5. Kg4 e2! and it is all over) 5... Re2 6. Kf4 Rxe8

This is the best that White could have achieved after his first move (Rf8). White hopes that he will be able to push his pawn forward quickly before the Black King sneaks up. Unfortunately, White's hopes are unrealizable.

7. g4 Kf2 8. g5 Rg8!! (A strong move which forces White to now use his King, which will allow the Black King to move up the board) 9. Kf5 Kg3 10. g6 Kh4 The Black King arrives in time.

11. Kf6 Kh5 12. g7 Kh6 And that is all there is to it; the reader can verify for himself that the White pawn is now lost

Returning to the initial position, White can draw if he retreats his rook to f7:

1. Rf7!! This paradoxical move allows White to save the game. This idea was missed by the players' teams in their published analysis!

Play proceeds normally: 1... Kd2! 2. Rd7 Ke1 3. Re7 Rd2 4. Kf3 Rf2

This position is the similar to the previous case, but with the little difference that here the White rook is on the 7th rank. It makes all the difference!

5. Kxe3!! ( Again, 5. Kg4 loses without a fight after 5... e2 6. Kh5 Rf3 7. g4 Kf2 8. Rxe2 (8. g5 Re3) 8... Kxe2 9. g5 Ke3 10. g6 Kf4)

5... Re2 6. Kf4 Rxe7 What is the difference between this and the previous case?

Here White is able to draw because he will be able to gain a tempo attacking the Black rook. Chess is like that: one tempo is the difference between being a hero or a duffer!

7. g4 Kf2 8. g5 Rg7 (Again, Black must try to find a way for his King to advance) 9. Kf5 Kg3 10. g6 Kh4 11. Kf6

And the game is clearly drawn now, as the reader can easily verify for himself; the Black King can not make it back in time and so Black will have to give up his rook for the pawn.

Summing up, only by avoiding making the natural rook retreat (f8), can White save the game. As a point of interest, the draw can be held by white retreating the rook to f5 or f6 also (but I will not show this here since it falls outside the scope of this article)

White can draw by moving his rook to any of the blue coloured squares!

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As a point of interest, the following position also came up in the analysis of the Kramnik vs Kasparov game, and once more their analysts got it all wrong! It was concluded that Black wins, but as Alain Villeneuve showed, it is a draw!

Here Black seems even better off than in the previous example: the White King is cut off on the 1st rank, his rook is attacked and must move, his pawn in only on the 3rd rank and black is threatening to advance is pawn. However, it is still a draw!! But the rook must not retreat to the natural square (g8)...





1. Rg8? This natural move is the only move considered by the Kramnik/Kasparov teams, and after this move White can no longer save his game.




Play would proceed:
1... e4 2. Rf8 Ke2 3. g4 e3 4. Kg2 Rd4 5. Kg3 Kd2 Black must try to Queen his pawn





6. Re8 (forced) 6... e2 7. Kf2 Rf4! A very important move; the King is driven away. There is no other way to make progress


8. Kg3 Rf8!! White was threatening just to advance his pawn and make a draw, so Black's only real chance is to deflect the White rook and take his chances in a Queen vs Rook and pawn ending (which in this case is winning, as we shall see)




9. Rxf8 e1Q 10. Kh3 Qe3! Beautiful! The threat of picking up the White rook (h6) forces White to make concessions.


11. Kg2 Qe7! 12. Rf5 Qh4! The Black Queen has managed to penetrate around the White pawn and it is soon evident that White loses material.



13. Kf3 Qh3 14. Kf4?? Qe3 mate!


BUT WHITE CAN DRAW IF HE MOVES HIS ROOK TO G7 !!:

As Alain Villeneuve showed, the correct idea is





1. Rg7!!



This move goes against our intuition, but is infact the way to draw.

1... e4 2. Rf7 Ke2 3. g4 e3 4. Kg2! Rd4 5. Kg3 Kd2 Everything proceeds as before

6. Re7 e2 7. Kf2 Rf4 8. Kg3 Rf7!? Black follows the same idea as in the previous case. Otherwise White will simply advance his pawn and the game will be a dead draw.

9. Rxf7 e1Q 10. Kh3 Qe3 And only now do we see the difference between having the rook on f7 or f8: with the rook on f7 Black does not threatent to pick up the rook with a check!! Subtle but effective.

11. Kg2 Qg5 (Black can not get his Queen to h4) 12. Kg3 Ke2 13. Rf5 White now has a well known theoretical draw

White has achieved a fortress, where the Black King can not break past the f-file and the Black Queen can not win the White pawn. The reader can verify this himself easily enough, or go and check in any table base.

Returning to the initial position, it should be mentioned for the sake of thoroughness that White can draw by moving his rook to any of the squares that are coloured blue in the diagram above. The technique in each case might vary, but is outside of the scope of this article to deal with. The essential point to remember is that any rook move other than g8 allows White to draw!

I believe that Alain Villeneuve's analysis of this ending is remarkable, and sheds much light on the secrets behind this class of ending. In my opinion, Villeneuve is one of the world's foremost authorities on the endgame, and I recommend the readers get a hand on his books!

Finally, I would like to recount to the readers a bit about my visit to Alain Villeneuve's home in Paris this past month. As explained in an earlier blog entry, I was invited to give some lectures at a club in Paris (which was successful) and on Wednesday Jean-luc Seret brought me to Alain's home.

Apparently every Wednesday (for the past 40 years!) Alain and a group of his friends get together to play chess, exchange ideas and analysis, take a look at games and what not. But especially, to look at endgame studies and problems! I was most impressed with the depth of knowledge of those who attended. I must confess that I was a bit out of my depth! I did not know how big and colourful the world of studies and compositions was. Being a practical tournament player at heart, I had neglected to notice all those players who don't play in tournaments but who find much fascination and enjoyment in creating studies and problems. Has any one of you readers ever heard of a chess problem that requires 25,000 moves to win? Amazing!

PS: (Wednesday 8,April) Alain Villeneuve's analysis can be found on a number of different sites (in French). The following is quite good:

http://www.france-echecs.com/index.php?mode=showComment&art=20061225181612247

As for the incorrect analysis of the Kramnik/Kasparov teams, check the informators from 2000 as a starting point. Some of the incorrect analysis is there. There are also other links, since the games' analysis was reproduced in hundreds, if not thousands, of sites immediately following the match. Then there have been 'improvements' by Kasparov himself put on the net since 2000, but they also contain errors.

It is important to remember that the 6 piece table bases did not exist in 2000, and infact only recently became available. I am certain , however, (even without the help of table bases)
had the analysts devoted more time and attention to the ending, that their errors would have been discovered.

That being said, rook and pawn endings are notoriously difficult to analyse. Even for great players like Kasparov and Kramnik. My view is that it takes years for these errors to be spotted (since few players are really willing to devote time to checking the analysis) and it is not unheard of that endings have been completely misunderstood for 50 years or more. We are human, after all, and that gives us the right to be wrong!

One last comment: even Kasparov's analysis of the famous Lasker vs Rubinstein ending from St.Petersburg in 1914(that is presented in one of his books on his predecessors) contains a few important flaws. Much of Kasparov's analysis in these books is just fritz and other programs...and these programs really can not play the ending with any degree of precision.

Proper endgame analysis can hardly compete with publishing deadlines...

SPRAGGETT ON CHESS